Method and apparatus for measuring motion of a suspended particle or a suspending fluid

A method for determining at least two particle motion parameters P.sub.1, P.sub.2, . . . of one or more sets of particle motion parameters, where each set defines motion of a particle in a specified direction at or near a specified time and, when desired, using the set(s) of particle motion parameters for determining one or more of, (I) one or more of at least one set of fluid motion parameters F.sub.1, F.sub.2, . . . which define motion of a fluid in at least one specified direction at or near a specified time, (II) at least one property of a particle, (III) at least one property of a fluid, and (IV) at least one external force acting on a particle in a specified direction or a derivative of this force with respect to time, comprising:

• a) observing a radiation signal from at least one particle, where the signal is at least one of an electromagnetic or acoustic radiation signal reflected, scattered or emitted from the particle;
• b) modulating the radiation signal from the particle by modulating the radiation illuminating or radiation from the particle, where the modulation causes the signal, or a signal derived therefrom, to contain at least one set of distinct features which repeat in time, an mth and an nth of which features of a set occur at times t.sub.m and t.sub.n separated by interval t.sub.mn =t.sub.m -t.sub.n which is a time interval from a reference time t.sub.n, where t.sub.m and t.sub.n may differ for different sets, and where a net displacement .DELTA..sub.mn of the particle in a specified direction during interval t.sub.mn is related to t.sub.mn by at least one equation .DELTA..sub.m =F(t.sub.mn), where F(t.sub.mn) is a known function of t.sub.mn for particle motion in at least one specified direction;
• c) detecting at least one modulated radiation signal from the particle or a signal derived therefrom to convert the at least one modulated radiation signal or the signal derived therefrom into at least one signal which can be processed;
• d) processing the at least one signal in a manner detecting at least one set of N+1 distinct features dependent on time t and on particle location x.sub.p in at least one specified x.sub.p -direction, where the distinct features in a set occur at times t.sub.j and locations x.sub.pj with j=1, 2, 3, . . . , N, N+1, N is a positive integer greater than one which may differ for different sets, and 1.ltoreq..+-.(m-n).ltoreq.N for each set;
• e) processing further the signal in a manner determining N of the t.sub.mn intervals between N unique pairs of the N+1 values of t.sub.j for at least one set of t.sub.j values corresponding to particle motion in at least one specified x.sub.p -direction, and (optionally) determining the values of X.sub.pj for j=1, 2, 3, . . . , N, N+1;
• f) processing further the signal determining at least one set of net displacements .DELTA..sub.mn =x.sub.pm -x.sub.pn of the particle in a specified x.sub.p -direction which occur during the set of N unique t.sub.mn intervals using an expression .DELTA..sub.mn =F(t.sub.mn) or (optionally) using .DELTA..sub.mn =x.sub.pm -x.sub.pn and the N+1 values of X.sub.pj ;
• and,
• g) utilizing the processed signals to solve a set of N equations relating .DELTA..sub.m and t.sub.mn values for motion in each specified x.sub.p -direction with each of the equations containing two or more particle motion parameters P.sub.1, P.sub.2, . . . of at least one set of particle motion parameters for particle motion in at least one specified x.sub.p -direction, which motion parameters are the only unknown quantities in the general equation ##EQU11## or an equivalent general equation, where index mn denotes in turn each of N (.DELTA..sub.mn, t.sub.mn) data pairs which give by the general equation the set of N equations, one mn-specific equation for each of the N mn data pairs, the Greek sigma denotes a sum over M terms for which index k takes values 1, 2, 3, . . . , M, M is an integer value selected to be equal to or greater than a desired number of particle motion parameters, particle motion parameter P.sub.k =d.sup.k x.sub.p /dt.sup.k is a kth derivative with respect to time of particle location x.sub.p at or near a specified time t.sub.n, and k!=1.times.2.times.3.times.. . . xk;
• and, when desired, one or more of,
• h1) determining at least one fluid motion parameter F.sub.k with k=1 or 2 or 3 or . . . for fluid motion in at least one specified x.sub.p -direction by solving at least one particle equation of motion
• F.sub.1 =P.sub.1 +(m.sub.p .times.P.sub.2 -G.sub.o /f,
• or an equivalent equation including one obtained by taking a kth derivative of this equation with respect to time, to obtain at least one fluid motion parameter F.sub.k =d.sup.k x.sub.f /dt.sup.k for a fluid element for at least one specified x.sub.p -direction with x.sub.f an x.sub.p -direction displacement of the fluid element at time t, m.sub.p is a known particle mass or is related in a known way to at least one other particle or fluid property, f is a known particle-fluid friction coefficient or is related in a known way to at least one particle or fluid property, G.sub.k-1 =d.sup.(k-1) G.sub.o /dt.sup.(k-1) is a known (k-1)st derivative with respect to time of an external force G.sub.o in a specified x.sub.p -direction, and P.sub.k and P.sub.k+1 are measured particle motion parameters for motion in a specified x.sub.p -direction;
• or,
• h2) determining at least one property of a particle suspended in a fluid at one or more times by measuring the values of particle motion parameters P.sub.1 and P.sub.2, or P.sub.k and P.sub.k+1, for a specified x.sub.p -direction and using the values in solving particle equation of motion
• m.sub.p /f=(F.sub.1 -P.sub.1 -G.sub.o /f)/P.sub.2,
• or an equivalent equation including one obtained by taking a kth derivative of the particle equation of motion with respect to time, to obtain one or more values of property m.sub.p /f or G.sub.o /f or of G.sub.o /m.sub.p or of one or more other properties using known values for the suspending fluid properties, at least one known fluid motion parameter F.sub.1 or F.sub.k for fluid motion in the specified x.sub.p -direction and either (i) a known (k-1)st derivative with respect to time G.sub.k-1 =d.sup.(k-1) G.sub.o /dt.sup.(k-1) of an external force G.sub.o in the specified x.sub.p -direction, or (ii) a known relationship between at least one particle property and a particle motion parameter and an external force or time-derivative thereof, G.sub.o or G.sub.(k-1), which is changeable multiple times during the course of multiple measurements of the particle motion parameters to provide data which is usable with the known relationship to determine multiple particle properties, with k=1 or 2 or 3 or . . . ;
• or,
• h3) determining at least one property of a fluid in which at least one particle is suspended by solving a particle equation of motion
• m.sub.p /f=(F.sub.1 -P.sub.1 -G.sub.o /f)/P.sub.2,
• or an equivalent equation including one obtained by taking a kth derivative with respect to time of this equation, to obtain one or more values of at least one fluid property for the case when two or more particle motion parameters P.sub.k and P.sub.k+1 for particle motion in a specified x.sub.p -direction are known, at least one fluid motion parameter F.sub.k for motion in the specified x.sub.p -direction is known, and one of (i) at least one external force G.sub.o in the specified x.sub.p -direction, or (ii) a (k-1)st derivative with respect to time of G.sub.o in the specified x.sub.p -direction, or (iii) a relationship between G.sub.O and at least one particle or fluid property is known for k=1 or 2 or 3 or . . . ;
• or,
• h4) determining one or more values of an external force G.sub.O acting on a particle in at least one specified x.sub.p -direction by solving a particle equation of motion
• G.sub.o =m.sub.p .times.P.sub.2 -f.times.(F.sub.1 -P.sub.1),
• or an equivalent equation including one obtained by taking a kth derivative with respect to time of this equation with k=1 or 2 or 3 or . . . , for the case when all quantities in the equation are known except G.sub.o or a derivative with respect to time thereof.